Effective behavior of linear viscoelastic composites containing aligned spheroidal particles : exact and reduced internal variables representations

This work investigates the effective response and stress fluctuations in two-phase particulate composites composed of a matrix containing spheroidal inclusions all aligned in the same direction, a configuration typical of short-fiber composites. Both phases, matrix and inclusions, are linear and viscoelastic of Maxwell type. The objective of the present study is twofold. The first aim is to extend to composites containing aligned spheroidal inclusions the results obtained by means of the correspondence principle in Lahellec et al. (2024a) for isotropic two-phase composites. It is shown that the composite behaves as a generalized Maxwell material which can be described by a finite number of internal variables. The stress fluctuations in the matrix can be derived from the effective thermodynamic functions of the composite. A second contribution of this study is the extension to transversely isotropic composites of the reduced model of Suquet (2012) which makes only use of information determined in the purely elastic or purely viscous regimes. The accuracy of the reduced model is assessed by comparison with the exact model derived by means of the correspondence principle and the agreement is found to be excellent.